Check if a number can be expressed as a sum of consecutive numbers in C++

Here we will see if one number can be represented as sum of two or more consecutive numbers or not. Suppose a number is 12. This can be represented as 3+4+5.

There is a direct and easiest method to solve this problem. If a number is power of 2, then it cannot be expressed as sum of some consecutive numbers. There are two facts that we have to keep in mind.

• Sum of any two consecutive numbers is odd, then one of them will be odd, another one is even.
• Second fact is 2ⁿ = 2^(n-1) + 2^(n-1).

Example

 Live Demo

#include <iostream> using namespace std; bool isSumofconsecutiveNumbers(int n) {    if((n & (n-1)) && n){       return true;    } else {       return false;    } } int main() {    int num = 36;    if(isSumofconsecutiveNumbers(num)){       cout << "Can be represented";    } else {       cout << "Cannot be represented";    } }

Output

Can be represented